Luxembourg’s Jean Asselborn portrayed it as an artificial outcome generated by the well-funded campaign of an individual mastermind, Christoph Blocher of the Swiss People’s Party, rather than a genuine reflection of the Swiss mood.

He indicated that anti-immigrant movements inside the EU, such as Geert Wilders’ PVV party in The Netherlands, Jean-Marie Le Pen’s Front National in France, and Heinz-Christian Strache’s FPO in Austria follow the same model.

“Mr Blocher, the chief of this idea, maybe has lots of money, but I think he is shortsighted. You can see the kind of people who share his ideas - Wilders, Le Pen, Strache - he’s in good company,” Asselborn said.

Ireland’s Eamon Gilmore delegitimised the Swiss vote as a form of xenophobia. “We are seeing signs of the rise of the extreme right in Europe,” he noted.

Belgium’s Didier Reynders admitted there is similar feeling in his country, but added that the scale in Switzerland is different. “It exists in all countries, so we must not stigmatise anyone, but it’s true that the majority [of the Swiss] expressed themselves in this way,” he said.

Germany’s Frank-Walter Steinmeier played down the political nature of the development.

With the German government in recent months also criticising EU “welfare tourism” amid rising euroscepticism ahead of the EU elections in May, he said: “We need to assess the consequences without foaming at the mouth … There will be technical reasons to reassess the existing [EU-Swiss] process.”

But France’s Laurent Fabius, whose Socialist party trails the Front National in polls, went on the attack.

He said Switzerland should be “punished,” adding that it is “not a considerable economic power” and that it “makes a good living off the EU.”

His junior minister in charge of EU affairs, Thierry Repentin, admitted that pro-EU politicians need to do more to win people’s hearts. But he added: “This [Swiss] vote … should not be extrapolated to say what people in Europe think of free movement.”

Noting that the UK recently questioned the rights of Bulgarians and Romanians to work in Britain, he said the matter is now closed: “Clearly, all the Europeans from all the 28 member states have the right to move to all the countries of the EU.”

But for their part, eurosceptic leaders in Belgium and in the UK, disagreed.

Filip Dewinter, from the Flemish hard-right nationalist party in Belgium, Vlaams Belang, told EUobserver also on Monday that the Swiss vote is “a very important signal.”

He said the rise in euroscepticism is linked to EU immigration policies and its unwillingness to address people’s fears. “What happened in Switzerland would be happening all over Europe, but only the Swiss have direct democracy with referendums, which makes it possible for people to express themselves,” he noted.

“This has nothing to do with racism … it’s about taking away people’s way of life, their culture,” he added.

Nigel Farrage, a founding member of the UK Independence Party (Ukip), also said the Swiss result could be easily replicated inside the EU.

He said one of the EU’s “fundamental mistakes” was to uphold freedom of movement when it let in the poorer, former Communist, countries in 2004, prompting large numbers to come to Britain and Ireland. “Freedom of movement was not an issue until 2004. People were quite relaxed about it, including myself,” he said.

The Swiss vote also highlighted the differences inside the eurosceptic camp, however.

For his part, the British foreign secretary kept a low profile in Brussels on Monday. William Hague said he “respects” the Swiss people’s choice, adding only: “We will be mindful of the position of the 40,000 British nationals who work in Switzerland."

With the Conservatives trying to steer a middle way between domestic politics and its EU commitments, Farrage accused Hague of not knowing where he stands.

“I don’t think the Conservative Party knows what its policy is on immigration. It eulogised the EU position up until six months ago and now it has changed tack completely in response to Ukip,” he said.